Efficient key management based on the subset difference method for secure group communication

A new algorithm for efficient key management for secure group communication in wireless ad hoc network with mobile nodes is presented. In order to address the dynamic receiver update operations such as leave or join, the subset difference (SD) method proposed by Naor et al. is introduced. The SD method allows senders to reduce drastically the size of ciphertext to be sent to 2r-1 using a pseudo random number generator, where r is the number of revoked users (who leave the group). In the SD method, the subsets of authorized users are represented by some differences of two subsets such that i covers valid users and j excludes the revoked users in i. To have all subsets (i,j) necessary to cover all valid users in a tree, a sender has to test all possible combinations of revoked users. A naive exhaustive search for the purpose takes O(r³) time. This is a drawback of the SD method. Hence, to address the issue for finding the cover, we propose a new efficient algorithm to reduce the cost up to O(rlog r logn) by introducing the technique for indexing nodes to be dealt with in the necessary subsets. In addition, we implement the proposed algorithm and demonstrate the performance in terms of processing time in this paper.